Advertisement

Flexible Distributed Lag Models Using Random Functions With Application to Estimating Mortality Displacement From Heat-Related Deaths

  • Matthew J. HeatonEmail author
  • Roger D. Peng
Article

Abstract

Changes in the distribution of ambient temperature, due to climate change or otherwise, will likely have a negative effect on public health. Characterizing the relationship between temperature and mortality is a key aspect of the larger problem of understanding the health effect of climate change. In this article, a flexible class of distributed lag models are used to analyze the effects of heat on mortality in four major metropolitan areas in the U.S. (Chicago, Dallas, Los Angeles, and New York). Specifically, the proposed methodology uses Gaussian processes to construct a prior model for the distributed lag function. Gaussian processes are adequately flexible to capture a wide variety of distributed lag functions while ensuring smoothness properties of process realizations. The proposed framework also allows for probabilistic inference of the maximum lag. Applying the proposed methodology revealed that mortality displacement (or, harvesting) was present for most age groups and cities analyzed suggesting that heat advanced death in some individuals. Additionally, the estimated shape of the DL functions gave evidence that highly variable temperatures pose a threat to public health. This article has supplementary material online.

Key Words

Climate change Gaussian process Harvesting Public health 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Supplementary material

13253_2012_97_MOESM1_ESM.pdf (91 kb)
Supplemental Materials A: Specifics of Markov chain Monte Carlo Algorithms (PDF 91 kB)
13253_2012_97_MOESM2_ESM.pdf (66 kb)
Supplemental Materials B: Additional Simulation Results (PDF 66 kB)

References

  1. Anderson, B. G., and Bell, M. L. (2009), “Weather-Related Mortality: How Heat, Cold, and Heat Waves Affect Mortality in the United States,” Epidemiology, 20, 205–213. CrossRefGoogle Scholar
  2. Banerjee, S., Carlin, B. P., and Gelfand, A. E. (2004), Hierarchical Modeling and Analysis for Spatial Data, London: Chapman and Hall/CRC. zbMATHGoogle Scholar
  3. Bell, M. L., Samet, J. M., and Dominici, F. (2004), “Time-Series Studies of Particulate Matter,” Annual Review of Public Health, 25, 247–280. CrossRefGoogle Scholar
  4. Braga, A. L., Zanobetti, A., and Schwartz, J. (2001), “The Time Course of Weather-Related Deaths,” Epidemiology, 12, 662–667. CrossRefGoogle Scholar
  5. — (2002), “The Effect of Weather on Respiratory and Cardiovascular Deaths in 12 U.S. Cities,” Environmental Health Perspectives, 110, 859–863. CrossRefGoogle Scholar
  6. Caffo, B. S., Peng, R. D., Dominici, F., Louis, T. A., and Zeger, S. L. (2011), “Parallel MCMC Imputation for Multiple Distributed Lag Models: A Case Study in Environmental Epidemiology,” in The Handbook of Markov Chain Monte Carlo, London: Chapman and Hall/CRC Press, pp. 493–511. Google Scholar
  7. Chib, S., and Jeliazkov, I. (2001), “Marginal Likelihood from the Metropolis–Hastings Output,” Journal of the American Statistical Association, 96, 270–281. MathSciNetzbMATHCrossRefGoogle Scholar
  8. Cressie, N., and Wikle, C. K. (2011), Statistics for Spatio-Temporal Data, New York: Wiley. zbMATHGoogle Scholar
  9. Curriero, F. C., Heiner, K. S., Samet, J. M., Zeger, S. L., Strug, L., and Patz, J. A. (2002), “Temperature and Mortality in 11 Cities of the Eastern United States,” American Journal of Epidemiology, 155, 80–87. CrossRefGoogle Scholar
  10. Frances, P. H., and van Oest, R. (2004), “On the Econometrics of the Koyck Model,” Technical Report, Economic Institute, Erasmus University Rotterdam. Google Scholar
  11. Haario, H., Saksman, E., and Tamminen, J. (2001), “An Adaptive Metropolis Algorithm,” Bernoulli, 2, 223–242. MathSciNetCrossRefGoogle Scholar
  12. Hajat, S., Armstrong, B. G., Gouveia, N., and Wilkinson, P. (2005), “Mortality Displacement of Heat-Related Deaths,” Epidemiology, 16, 613–620. CrossRefGoogle Scholar
  13. Handcock, M. S., and Stein, M. L. (1993), “A Bayesian Analysis of Kriging,” Technometrics, 35, 403–410. CrossRefGoogle Scholar
  14. Handcock, M. S., and Wallis, J. (1994), “An Approach to Statistical Spatial-Temporal Modeling of Meteorological Fields (With Discussion),” Journal of the American Statistical Association, 89, 368–390. MathSciNetzbMATHCrossRefGoogle Scholar
  15. IPCC (2007), Climate Change 2007: Impacts, Adaptation and Vulnerability. Contribution of Working Group II to the Fourth Assessment Report of the Intergovernmental Panel on Climate Change, Cambridge: Cambridge University Press. Google Scholar
  16. Kovats, R. S., and Hajat, S. (2008), “Heat Stress and Public Health: A Critical Review,” Annual Review of Public Health, 29, 41–55. CrossRefGoogle Scholar
  17. Li, B., Sain, S., Mearns, L. O., Anderson, H. A., Kovats, S., Ebi, K. L., Bekkedal, M., Kanarek, M. S., and Patz, J. A. (2011), “The Impact of Extreme Heat on Morbidity in Milwaukee, Wisconsin,” Climatic Change. doi: 10.1007/s10584-011-0120-y. Google Scholar
  18. Matérn, B. (1986), Spatial Variation (2nd ed.), Berlin: Springer. zbMATHGoogle Scholar
  19. Meehl, G. A., and Tebaldi, C. (2004), “More Intense, More Frequent, and Longer Lasting Heat Waves in the 21st Century,” Science, 305, 994–997. CrossRefGoogle Scholar
  20. O’Neill, M. S., Zanobetti, A., and Schwartz, J. (2003), “Modifiers of the Temperature and Mortality Association in Seven US Cities,” American Journal of Epidemiology, 157, 1074–1082. CrossRefGoogle Scholar
  21. Peng, R. D., Bobb, J. F., Tebaldi, C., McDaniel, L., Bell, M. L., and Dominici, F. (2011), “Toward a Quantitative Estimate of Future Heat Wave Mortality Under Global Climate Change,” Environmental Health Perspectives, 119, 701–706. CrossRefGoogle Scholar
  22. Peng, R. D., Dominici, F., and Welty, L. J. (2009), “A Bayesian Hierarchical Distributed Lag Model for Estimating the Time Course of Risk Hospitalization Associated With Particulate Matter Air Pollution,” Journal of the Royal Statistical Society. Series C. Applied Statistics, 58, 3–24. MathSciNetCrossRefGoogle Scholar
  23. Roberts, S. (2005), “An Investigation of Distributed Lag Models in the Context of Air Pollution,” Journal of the Air & Waste Management Association, 55, 273–282. CrossRefGoogle Scholar
  24. Samet, J. M., Zeger, S. L., Dominici, F., Curriero, F., Coursac, I., Dockery, D. W., Schwartz, J., and Zanobetti, A. (2000), “The National Morbidity, Mortality, and Air Pollution Study Part II: Morbidity and Mortality From Air Pollution in the United States,” Research Report—Health Effects Institute, 94, 5–79. Google Scholar
  25. Schwartz, J. (2000), “The Distributed Lag Between Air Pollution and Daily Deaths,” Epidemiology, 11, 320–326. CrossRefGoogle Scholar
  26. Tebaldi, C., Hayhoe, K., Arblaster, J. M., and Meehl, G. A. (2006), “Going to the Extremes: An Intercomparison of Model-Simulated Historical and Future Changes in Extreme Events,” Climatic Change, 79, 185–211. CrossRefGoogle Scholar
  27. van Dyk, D. A., and Park, T. (2008), “Partially Collapsed Gibbs Samplers: Theory and Methods,” Journal of the American Statistical Association, 103, 790–796. doi: 10.1198/016214508000000409. MathSciNetzbMATHCrossRefGoogle Scholar
  28. Welty, L. J., Peng, R. D., Zeger, S. L., and Dominici, F. (2009), “Bayesian Distributed Lag Models: Estimating the Effects of Particulate Matter Air Pollution on Daily Mortality,” Biometrics, 65, 282–291. MathSciNetzbMATHCrossRefGoogle Scholar
  29. Welty, L. J., and Zeger, S. L. (2005), “Are the Acute Effects of Particulate Matter on Mortality in the National Morbidity, Mortality, and Air Pollution Study the Result of Inadequate Control For Weather and Season? A Sensitivity Analysis Using Flexible Distributed Lag Models,” American Journal of Epidemiology, 162, 80–88. CrossRefGoogle Scholar
  30. Zanobetti, A., Wand, M. P., Schwartz, J., and Ryan, L. M. (2000), “Generalized Additive Distributed Lag Models: Quantifying Mortality Displacement,” Biostatistics, 1, 279–292. zbMATHCrossRefGoogle Scholar
  31. Zhang, H. (2004), “Inconsistent Estimation and Asymptotically Equal Interpolations in Model-Based Geostatistics,” Journal of the American Statistical Association, 99, 250–261. MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© International Biometric Society 2012

Authors and Affiliations

  1. 1.Institute for Mathematics Applied to GeosciencesNational Center for Atmospheric ResearchBoulderUSA
  2. 2.Department of BiostatisticsJohns Hopkins Bloomberg School of Public HealthBaltimoreUSA

Personalised recommendations